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AlexanderFabisch committed Sep 29, 2024
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15 changes: 8 additions & 7 deletions doc/source/user_guide/transformations.rst
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Expand Up @@ -196,13 +196,13 @@ coordinates of transformation and typically we use the variable name Stheta.
.. warning::

Note that we use the screw theory definition of exponential coordinates
and :math:`se(3)` (see next section) used by Paden (1985), Lynch and Park
(2017), and Corke (2017). They separate the parameter :math:`\theta` from
and :math:`se(3)` (see next section) used by Lynch and Park (2017) [1]_,
and Corke (2017) [2]_. They separate the parameter :math:`\theta` from
the screw axis. Additionally, they use the first three components to encode
rotation and the last three components to encode translation. There is an
alternative definition used by Eade (2017) and Sola et al. (2018). They use
a different order of the 3D vector components and they do not separate
:math:`\theta` from the screw axis in their notation.
alternative definition used by Eade (2017) [3]_ and Sola et al. (2018)
[4]_. They use a different order of the 3D vector components and they do
not separate :math:`\theta` from the screw axis in their notation.

---------------------------
Logarithm of Transformation
Expand Down Expand Up @@ -251,8 +251,9 @@ Twist

We call spatial velocity (translation and rotation) **twist**. Similarly
to the matrix logarithm, a twist :math:`\mathcal{V} = \mathcal{S} \dot{\theta}`
is described by a screw axis :math:`S` and a scalar :math:`\dot{\theta}`
and :math:`\left[\mathcal{V}\right] = \left[\mathcal{S}\right] \dot{\theta} \in se(3)`
is described by a screw axis :math:`\mathcal S` and a scalar
:math:`\dot{\theta}` and
:math:`\left[\mathcal{V}\right] = \left[\mathcal{S}\right] \dot{\theta} \in se(3)`
is the matrix representation of a twist.

----------------
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